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Minimization of the Ratio of Functions Defined as Sums of the Absolute Values

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Abstract

This paper addresses a new class of linearly constrained fractional programming problems where the objective function is defined as the ratio of two functions which are the sums of the absolute values of affine functions. This problem has an important application in financial optimization.

This problem is a convex-convex type of fractional program which cannot be solved by standard algorithms. We propose a branch-and-bound algorithm and an integer programming algorithm. We demonstrate that a fairly large scale problem can be solved within a practical amount of time.

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Authors and Affiliations

  1. Department of Industrial and Systems Engineering, Chuo University, Tokyo, Japan

    H. Konno, K. Tsuchiya & R. Yamamoto

  2. Mitsubishi UFJ Trust Investment Technology Institute Company, Tokyo, Japan

    R. Yamamoto

Authors
  1. H. Konno
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  2. K. Tsuchiya
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  3. R. Yamamoto
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Corresponding author

Correspondence to R. Yamamoto.

Additional information

Communicated by S. Schaible.

The research of the first author was supported in part by the Grant-in-Aid for Scientific Research of the Ministry of Education, Science, Culture and Sports of the Government of Japan, B(2) 15310122 and 15656025.

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Konno, H., Tsuchiya, K. & Yamamoto, R. Minimization of the Ratio of Functions Defined as Sums of the Absolute Values. J Optim Theory Appl 135, 399–410 (2007). https://doi.org/10.1007/s10957-007-9284-z

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  • DOI: https://doi.org/10.1007/s10957-007-9284-z

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